Approximate controllability for abstract measure differential systems

Wan, Xiaojun

doi:10.1016/j.sysconle.2011.09.014

Cited by 9 publications

(9 citation statements)

References 16 publications

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“…On the other side, Wan and Sun 19 studied approximate controllability for abstract MDEs in Banach space setting. In 2018, Cao and Sun 20 extended the results for approximate controllability of nonlinear MDEs via Schauder's FPT.…”

Section: Introductionmentioning

confidence: 99%

Approximate controllability of time varying measure differential problem of second order with state-dependent delay and non-instantaneous impulse

Kumar

2022

Preprint

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It is comprehended that the systems without any limitation on their Zeno action are enthralled in a vast class of hybrid systems. This article is influenced by a new category of non-autonomous second order measure differential problems with state-dependent delay (SDD) and non-instantaneous impulse (NII). Some new sufficient postulates are created that guarantee solvability and approximate controllability. We employ the fixed point strategy and theory of Lebesgue–Stieltjes integral in the space of piecewise regulated functions. The measure of non-compactness is applied to establish the existence of a solution. Moreover, the measured differential equations generalize the ordinary impulsive differential equations. Thus, our findings are more prevalent than that encountered in the literature. At last, an example is comprised that exhibits the significance of the developed theory.

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Section: Introductionmentioning

confidence: 99%

Approximate controllability of time varying measure differential problem of second order with state-dependent delay and non-instantaneous impulse

Kumar

2022

Preprint

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“…Recently the theory of controllability has attracted many authors, e.g., [32][33][34]. Wan and Sun considered the approximate controllability for abstract measure differential systems (see [35]), Cao and Sun in [36] discussed the complete controllability of measure differential equations by using Monch fixed point theorem and noncompact measure. Measure differential equation has developed rapidly, but it mainly focuses on integer order, there are few results on fractional order.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal controllability of fractional measure evolution equation

Sun

2020

J Inequal Appl

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In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: C D α 0+ x(t) = Ax(t) dt + (f (t, x(t)) + Bu(t)) dg(t), t ∈ (0, b], x(0) + p(x) = x 0. The regulated proposition of fractional equation is obtained for the first time. By noncompact measure method and fixed point theorems, we obtain some sufficient conditions to ensure the existence and nonlocal controllability of mild solutions. Finally, an illustrative example is given to show practical usefulness of the analytical results.

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“…Impulsive differential equation, which provides a natural description of observed evolution processes, is an important mathematical tool to solve some practical problems. The theory of impulsive differential equations of integer order has been widely used in practical mathematical modeling and has become an important area of research in recent years, which steadily receives attention of many authors (see [21][22][23][24][25][26][27][28][29][30][31][32][33][34]). Sun et al [35] considered a class of impulsive fractional differential equations with Riemann-Liouville fractional derivative, the existence of solution was proved by using Darbo-Sadovskii's fixed-point theorem, and the optimal control results were obtained.…”

Section: Introductionmentioning

confidence: 99%

Optimal Controls for a Class of Impulsive Katugampola Fractional Differential Equations with Nonlocal Conditions

Chen

Sun

2020

Journal of Function Spaces

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In this paper, we investigate a class of impulsive Katugampola fractional differential equations with nonlocal conditions in a Banach space. First, by using a fixed-point theorem, we obtain the existence results for a class of impulsive Katugampola fractional differential equations. Secondly, we derive the sufficient conditions for optimal controls by building approximating minimizing sequences of functions twice.

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Approximate controllability for abstract measure differential systems

Cited by 9 publications

References 16 publications

Approximate controllability of time varying measure differential problem of second order with state-dependent delay and non-instantaneous impulse

Approximate controllability of time varying measure differential problem of second order with state-dependent delay and non-instantaneous impulse

Nonlocal controllability of fractional measure evolution equation

Optimal Controls for a Class of Impulsive Katugampola Fractional Differential Equations with Nonlocal Conditions

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